Studies on double beta decay processes in 106Cd were performed by using a cadmium tungstate scintillator enriched in 106Cd at 66% (106CdWO4) with two CdWO4 scintillation counters (with natural Cd composition). No effect was observed in the data that accumulated over 26,033 h. New improved half-life limits were set on the different channels and modes of the 106Cd double beta decay at level of limT1/2∼1020−1022 yr. The limit for the two neutrino electron capture with positron emission in 106Cd to the ground state of 106Pd, T1/22νECβ+≥2.1×1021 yr, was set by the analysis of the 106CdWO4 data in coincidence with the energy release 511 keV in both CdWO4 counters. The sensitivity approaches the theoretical predictions for the decay half-life that are in the range T1/2∼1021−1022 yr. The resonant neutrinoless double-electron capture to the 2718 keV excited state of 106Pd is restricted at the level of T1/20ν2K≥2.9×1021 yr.